Exhibit 99.1

CERTIFICATION PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

(18 U.S.C. SECTION 1350)

Pursuant to 18 U.S.C. § 1350, the undersigned Chief Executive Officer of SWS Group, Inc. (the “Company”) hereby certifies:

(i)  that the Company’s Annual Report on Form 10-K for the fiscal year ended June 28, 2002 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(ii)  that information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/    DONALD W. HULTGREN      

Donald W. Hultgren

Chief Executive Officer

Dated:    September 26, 2002